Pooled-sample testing as a herd-screening tool for detection of bovine viral diarrhea virus persistently infected cattle

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1 J Vet Diagn Invest 1: (000) Pooled-sample testing as a herd-screening tool for detection of bovine viral diarrhea virus persistently infected cattle Claudia A. Muñoz-Zanzi, Wesley O. Johnson, Mar C. Thurmond, Sharon K. Hietala Abstract. The study was conducted to develop methodology for least-cost strategies for using polymerase chain reaction (PCR)/probe testing of pooled blood samples to identify animals in a herd persistently infected with bovine viral diarrhea virus (BVDV). Cost was estimated for 5 protocols using Monte Carlo simulations for herd prevalences of BVDV persistent infection (BVDV-PI) ranging from 0.5% to 3%, assuming a cost for a PCR/probe test of $0. The protocol associated with the least cost per cow involved an initial testing of pools followed by repooling and testing of positive pools. For a herd prevalence of 1%, the least cost per cow was $.64 (95% prediction interval $1.7, $3.68), where pool sizes for the initial and repooled testing were 0 and 5 blood samples per pool, respectively. Optimization of the least cost for pooled-sample testing depended on how well a presumed prevalence of BVDV-PI approximated the true prevalence of BVDV infection in the herd. As prevalence increased beyond 3%, the least cost increased, thereby diminishing the competitive benefit of pooled testing. The protocols presented for sample pooling have general application to screening or surveillance using a sensitive diagnostic test to detect very low prevalence diseases or pathogens in flocs or herds. Bovine viral diarrhea virus (BVDV) infection has been described as one of the most important cattle diseases in America. 4 Cattle that are immunotolerant and persistently infected (PI) with the virus are believed to shed the virus for life and may be responsible for maintaining the infection in the herd by continued exposure of susceptible animals to the virus. 14,15,5 An important element of BVDV control, therefore, is identification and removal of PI cattle from the herd. 1,3 Unfortunately, the many diagnostic techniques available to detect individual BVDV-infected cattle are costly, often maing their application impractical for identifying PI cattle in large herds, especially when the prevalence of persistent infection can be expected to be as low as 1 %. 1,13 Pooled testing to estimate prevalence and to identify infected individuals has been proposed as a cost-efficient approach for diseases with low prevalence, 8,11,4 including HIV, Chlamydia trachomatis, and hepatitis B infections in humans.,6,7,9,10,16,18 0,6 In veterinary diagnostic medicine, pooled testing has been used to identify Salmonella enteritidis in eggs, Trichinella spiralis in pigs, and hypodermosis and bovine leuemia virus infection in cattle. 5,17,,3 Among diagnostic techniques available for detection of BVDV, polymerase chain reaction (PCR) is well From the Department of Medicine and Epidemiology, School of Veterinary Medicine (Muñoz-Zanzi, Thurmond), and the Division of Statistics (Johnson), University of California, Davis, CA 95616, and the California Veterinary Diagnostic Laboratory System, Davis, CA (Hietala). Received for publication December 14, suited to pooled-sample testing based on the ability to detect very low levels of virus. Results can be obtained in a relatively short time, and according to preliminary validation, the technique has a very high diagnostic sensitivity and specificity. A critical step in designing a diagnostic approach involving pooling of samples is determining the procedure with the fewest number of tests required, thus with the lowest possible cost, to identify all animals persistently infected with BVDV (BVDV-PI animals) in a herd. If pool size is too large, there is an increased chance that any single pool will test positive, requiring additional testing to identify the 1 or viremic individuals in the positive pool. If the samples are grouped in unnecessarily small pools, the cost benefit of pooling samples is lost to the large number of negative pools tested for each positive pool identified. The objective of the present study was to identify and characterize testing protocols and corresponding optimal pool sizes that minimize the number of PCR tests required to identify all BVDV-PI cattle in a herd having prevalences of infection ranging from 0.5% to 3.0%. Methods The general approach taen was to estimate the cost associated with 5 protocols applying different strategies of pooling samples, including splitting and repooling of positive pools for various herd prevalences of BVDV-PI. The goal was to find the most cost-effective strategy for identifying BVDV-viremic animals, presumed to be PI, in a herd by comparing the least cost per cow obtained for different sample pooling protocols. The least cost was obtained by 195

2 196 Muñoz-Zanzi et al. finding the pool size that, on average, would require the fewest PCR tests to detect all BVDV-viremic cattle in a herd with a given prevalence of infection. BVDV PCR/probe assay BVDV genome was detected in whole blood samples using previously published primer sequences. 1 During development of the pooling procedure, single PI animals were detectable in pools of negative samples. To decrease the probability of false-negative results due to virus dilution in the pooling protocols, the maximum number of samples assigned to a pool was 80. For the purpose of presenting the pooling methodology in the simplest mathematical form, sensitivity and specificity of BVDV PCR were assigned values of 100%. Assumptions. The cost of one BVDV PCR/probe test, c, was assigned $0, based on estimates of reagent cost and technician time for sample extraction, PCR, and detection by probe. The cost was considered to be the same whether the PCR and subsequent probe detection test was performed on a pool of samples or on an individual animal sample. The total cost of testing a herd was represented as C herd, and the cost of testing a pool as C pool. The probability of disease, Pr(D), was the true prevalence of BVDV viremia in the herd, evaluated at 0.5%, 1.0%, 1.5%,.0%,.5%, and 3.0% for each protocol. The total number of animals tested was represented as N, the number of samples per pool (pool size) as, and the number of pools as r, where r N/, assuming the quotient N/ is an integer. To simplify calculations, herd size was set at N 1,000, and average cost per cow was calculated as E(C herd )/N, where E(C herd ) is the expected cost of testing the whole herd. Each pool was assumed to constitute a random sample, where each individual animal blood sample would have probability of testing positive by BVDV PCR/probe. The number of positive samples in a pool was j, where 0 j. Because BVDV infection prevalence is typically expected to be no greater than % 1,13 and samples are randomly allocated to pools, the probability of positive samples in a pool is negligible ( ). A positive pool was assumed to have at least 1 viremic animal in the pool, and the probability that a pool would test positive was the binomial probability, p 1 (1 ), which is a monotonically increasing function of ; the higher the prevalence, the more liely a pool will test positive. The maximum lielihood estimator for p is pˆ x/r (the proportion of positive pools), 6 where x is the number of positive pools obtained from r tested pools, and x has a binomial distribution (r, p). If a pool tested negative, it was assumed that none of the cows represented in the pool were viremic, which occurs with probability (1 ). Estimation of cost. Total cost for identifying all individual BVDV-infected animals in a herd was estimated by approaches; an analytic approach using probability theory, and another approach using Monte Carlo simulations. By probability theory, the expected or average total herd cost is calculated as the number of initial pools tested multiplied by the expected or average cost per initial pool. The expected or average cost per initial pool is calculated as the cost per PCR/probe test multiplied by the average number of PCR/probe tests per initial pool. The average number of PCR/probe tests per initial pool includes the first PCR/probe test of the pool plus the subsequent PCR/probe tests required to identify all infected animals in the initial pool. Total herd cost calculated by the analytic approach was used to validate costs obtained by the Monte Carlo simulations. Monte Carlo simulations were generated to mimic the actual pooled testing process of herds of size N, with a BVDV prevalence of, using r pools of size. A computer program was written in S-Plus a that randomly selected r pools, each of size, from a binomial (, ) distribution, which would mimic the random allocation in the laboratory of N samples to r pools of size. (Computer programs written for Monte Carlo simulations are available upon request from C. Muñoz-Zanzi.) The total cost for each of the 7 protocols is obtained by applying the strategy of each testing protocol to the r pools generated. This procedure of randomly selecting r pools was repeated 5,000 times, which would be equivalent to testing a large number of herds with the same BVDV prevalence. The total cost obtained from each iteration would be similar to the actual selection of a herd and subsequent total cost calculation, and the collection of all 5,000 total costs should be distributed about the expected total cost obtained using probability theory. Simulations also provided a prediction interval for the total cost, where a 95% interval was the.5 and 97.5 percentiles of the total cost distribution. The 95% prediction interval corresponds to the range in which the total cost would fall 95% of the time and thus gives a range of costs that would be highly liely to occur in testing an actual herd. Because true herd prevalence for any infectious agent is unnown and some presumption or educated guess of the prevalence is necessary to determine the least-cost pooling strategy, the effect on cost of differences between presumed and true prevalence was characterized. The effect on cost was described for a population of herds with the same true prevalence among all herds and for a population of herds where the prevalence of infection is concentrated at about 1% and the probability of herds with prevalences 3% is very small. The prevalence of the latter herd population was assumed to have a statistical distribution (4.63, 360.6), which corresponds to a distribution of herds with a mode of 1% and a 99% certainty that the prevalence is 3%. Strategies for testing Protocol 1: simple pooling. The simplest method evaluates the samples in pools of size from a herd with prevalence. If the pool is PCR/probe positive, all the samples in the pool are tested individually to identify the viremic cow(s) (Fig. 1a). The total expected cost of pooled testing with this protocol, E(C herd ), is the product of the number of initial pools (r) times the expected cost per pool, where E(C pool ) is the cost (c) times the expected number of tests. As determined elsewhere, 10 the expected number of tests is 1 times the probability that the pool tests negative, (1 ), plus the number of tests for a positive pool, ( 1), times the probability that the pools test positive, [1 (1 ) ]. Therefore, the expected total cost for simple pooling is expressed as

3 Pooled testing to diagnose BVDV-PI 197 Figure 1. Representation of methods for pooled testing of samples from a herd to identify individual cattle infected with BVDV. Shaded figures represent positive test result. 7 Herd of size N. Samples tested in pools of size. # Split pools of size /. Split pools of size /4. 9 Repooled samples from positive pools. 8 Samples allocated to pools of size *. Split pools of size */. Test of individual samples. * E(C ) r{c(1 ) c( 1)[1 (1 ) herd ]}, which simplifies to E(C ) rc[( 1) (1 ) herd ]. (1) The total cost for a herd is thus a function of the herd size (N), pool size (), the true prevalence of BVDV viremia ( ), and the cost of performing a PCR/probe test (c). Costs were obtained for ranging from 1 to 30. Protocol : initial pooling of samples and 1 split of positive pools. Protocol is the same as protocol 1 except that positive pools are split in half by randomly allocating the samples to smaller pools, each of size /, which are then tested again. In this protocol, values were all even numbers from to 30. Samples from the smaller positive pools are tested individually to identify viremic animal(s) (see Fig. 1b). The potential benefit of splitting the positive pools obtained in an initial sequence of testing is that fewer tests would be expected if negative samples are randomly allocated to the same smaller pool. The expected or average cost associated with each initial pool considers all costs necessary to identify all viremic animals in the pool, including the first test of each initial pool, the tests after splitting, and the subsequent testing of individual samples. Only 1 test is required if the pool tests negative, which occurs with probability (1 ). If the pool tests positive, the cost depends on the number of positive samples in the pool (j). The expected cost associated with each pool is expressed as E(C ) c(1 ) pool c (1 m j) j 1 Pr(exactly j viremic samples in the pool), () where m j is the expected number of subsequent tests after splitting the first positive pool with j positive samples. The probability of j positive samples in a pool is the binomial probability Pr(exactly j infected samples in a pool) j(1 ) j. (3) j The number of tests per initial pool of size with only 1 positive sample is m1. (4) If the initial positive pool contains exactly positive samples, however, the expected number of subsequent tests is m ( )Pr(the positive samples are randomly allocated to each of the split pools) ( /)Pr(the positive samples are randomly allocated to the same split pool). The probability that the positive samples are randomly allocated to each of the split pools is 1 / 1 /. ( 1) The probability that the positive samples are randomly allocated to the same split pool is

4 198 Muñoz-Zanzi et al. / 1. ( 1) ( 1) / Therefore, 1 m ( ) ( 1) (5) ( 1) 4 Because the probability of j 3 or more positive samples in a pool would be very small for small (for example, the probability of j 3 in a pool of size 0 for a prevalence of 3% is ), we approximated the expected cost of a pool, E(C pool ), as [ E(C ) c (1 ) (1 m ) (1 ) 1 pool 1 1 (1 m ) (1 ). (6) The expected total cost of testing the herd, E(C herd ), is the number of initial pools (r) times the expected cost associated with each initial pool, which is re(c pool ). Protocol 3: initial pooling of samples and splits of positive pools. This protocol extends the approach of protocol by including a subsequent split of positive pools identified after a first split. Initial testing is done on pools of size, which correspond to all multiples of 4 from 4 to 8. If a pool tests positive, the pool is split into pools of size /. A positive split pool is split again to form pools of size /4, and samples of positive pools obtained at this step are tested individually to identify infected cow(s) (see Fig. 1c). The expected cost per initial pool, E(C pool ), with subsequent splits of positive pools is approximated as [ E(C ) c (1 ) (3 m ) (1 ) 1 pool 1 1 ] (3 m ) (1 ), (7) provided that is small, where the expected number of tests for a positive pool is the sum of the first 3 tests plus the expected number of tests after the first split. For 1 positive sample in a pool, the expected number of tests after the first split of pools is m1. (8) 4 The expected number of tests per initial positive pool with exactly positive samples is m (4 /)Pr(the positive samples are randomly allocated to each of the split pools at the first split) ( /4)Pr(the positive samples are randomly allocated to the same split pool at the first and second split) ( /)Pr(the positive samples are randomly allocated to the same split pool at the first split and to each ] of the split pools at the second split). The probability that the positive samples are randomly allocated to each of the split pools at the first split is /( 1). The probability that the positive samples are randomly allocated to the same split pool at the first split is / ( ). ( 1) / The probability that positive samples are randomly allocated to the same split pool at the second split is / /4 ( 4). / ( ) /4 The probability that the positive samples are randomly allocated to each of the split pools at the second split is / 1 /4 1 / /4. ( ) Therefore, m [ ] 4 ( 1) 4 [ ][ ] 4 ( 1) ( ) [ ][ ], ( 1) ( ) which simplifies to m. (9) ( 1) 16 4 The expected total cost of testing the herd will be the number of pools times the expected cost per pool, which is re(c pool ). Protocol 4: initial pooling of samples and repooling of positive pools. As with the other protocols, pools of size from a herd with prevalence are tested initially in a first stage to identify positive pools. Protocol 4 incorporates a second stage in which samples from the positive pools are randomly allocated to new pools of the same or smaller size than the first stage pools, where second stage pool size is *. The new pools are tested, and the individual samples comprising the positive pools are tested to identify viremic cows (see Fig. 1d). The expected total cost for this method of pooled testing, using probability theory, is mathematically intractable because of the numerous different pathways positive samples could follow. To avoid complex analytic calculations, the total expected cost for various prevalences and combinations of first and second stage pool sizes were ap-

5 Pooled testing to diagnose BVDV-PI 199 Figure. Cost per cow to identify BVDV-infected animals using protocol 1 for herd prevalences of 0.5%, 1.0%, 1.5%,.0%,.5%, and 3.0%, assuming cost of a PCR test is $0. least-cost pool size. proximated using Monte Carlo simulations, as described above. Simulations considered the various combinations of pool sizes for first-stage pools of size 1, 0, or 30 and for second-stage pool of sizes * that were factors of (e.g., for 1, *, 3, 4, 6, 1). Protocol 5: initial pooling of samples, repooling of positive pools, and 1 split of new positive pools. This protocol extends protocol 4 by splitting in half the positive pools identified at the second stage. The positive pools of size * are split to obtain pools of size */ that are then tested. Samples from positive pools of size */ are tested individually to identify viremic animal(s) (see Fig. 1e). Total cost was obtained as in protocol 4. Results The similar results obtained for Monte Carlo simulations and analytic calculations in protocols 1 3 validated use of Monte Carlo simulations, where differences in cost per cow for all 3 protocols ranged from $0 to $0.0. Because Monte Carlo simulations closely approximated costs obtained from analytic calculations and 1 method was required to permit comparisons, all protocols were compared based on results from Monte Carlo simulations only. Effect of prevalence and pool size on least cost. In all 5 protocols, cost increased as prevalence increased, and for any given prevalence, the cost decreased to a minimum and then increased, as pool size increased. The relationships among cost, prevalence, and optimum pool size are illustrated using the simplest method (protocol 1; Fig. ). The least-cost pool sizes for prevalences of 0.5%, 1.0%, 1.5%,.0%,.5%, and 3% were 15, 11, 8, 8, 7, and 6 blood samples, respectively, indicating that as prevalence increased the least-cost pool size decreased. The difference between the cost obtained using the least-cost pool size and that obtained for either a larger or a smaller pool size increased as prevalence increased. For example, the least cost per cow using protocol 1 with 0.5% prevalence and the corresponding least-cost pool size ( 15) was $.80. This cost differed by only $0.05 for protocol 1 with a pool size of 1 (cost per cow $.85) and by $0.07 with a pool size of 18 (cost per cow $.87). In contrast, the least cost per cow for a prevalence of % ($5.48; 8) differed by $0.44 for a pool size of 5 (cost per cow $5.9) and by $0.34 for a pool size of 11 (cost per cow $5.8). Effect of protocol on least cost. Table 1 presents the costs that would be obtained using protocols 1 5 when the prevalence is assumed to be nown (presumed prevalence true prevalence) and the appropriate least-cost pool size is used. Protocols incorporating retesting and repooling (protocols 5) yielded lower least costs per cow as compared with simple pooling (protocol 1). For prevalences ranging from 0.5% to.0%, the lowest cost per cow was obtained when samples in positive pools were repooled and new positive pools were split (protocol 5). For prevalences of.5% and 3%, protocol 4 yielded a slightly lower cost per cow than did protocol 5. Using protocol 5, the least costs per cow were $1.63, $.53, $3.33, $4.06, $4.74, Table 1. Average cost per cow associated with true prevalence of viremic cattle and least-cost pool sizes () to identify BVDV-infected cattle in a herd of N 1,000 cattle using protocols 1 5 for various herd prevalences. True prevalence (%) Protocol 1 Cost ($) Protocol Cost ($) Protocol 3 Cost ($) Protocol 4 Cost ($), * 95% P.I. Protocol 5 Cost ($), * , 6 $ , , 5 $ , , 5 $ , , 5 $ , , 4 $ , , 4 $ , 6 is first stage pool size, and * is second stage pool size. 95% P.I. 95% prediction interval.

6 00 Muñoz-Zanzi et al. Table. Effect on cost per cow ($) of differences between the presumed and true prevalence of BVDV-infected cattle for true prevalences of 0.5% and 3.0% using protocols 1 5. Presumed prevalence (%) True prevalence 0.5% True prevalence 3% and $5.31 for prevalences of 0.5%, 1.0%, 1.5%,.0%,.5%, and 3.0%, respectively. The costs per cow using protocol 4 for prevalences of.5% and 3% were $4.73 and $5.5, respectively. As prevalence was increased beyond 3%, the least costs per cow and 95% prediction intervals obtained for protocol 4 were $5.93 ($4.66 $7.6), $6.40 ($5.10 $7.78), $6.9 ($5.58 $8.30), $7.43 ($6.0 $8.88), $7.91 ($6.48 $9.40), and $8.40 ($6.94 $9.88) for prevalences of 3.5%, 4.0%, 4.5%, 5.0%, 5.5%, and 6.0%, respectively. The corresponding 95% prediction intervals for costs per cow, using protocols 1 5, for any given prevalence showed similar variation around the mean cost. The average difference between the mean and lower and upper limits over all prevalences and pool sizes was $1.14. Effect of selection of pool size on variation in cost. Two situations were examined to determine pool size to be used and the associated variation in cost: one that used the least-cost pool size for a presumed herd prevalence of infection and, consequently, considered the variation in cost when presumed prevalence differed from true prevalence and the other that used 1 pool size for all herds regardless of prevalence. Use of protocols 1 5 involves maing presumptions of herd prevalence, where these presumptions may be correct as assumed above or not. The average cost per cow, if the true prevalence was higher than the presumed prevalence, was more than the expected cost for a correctly presumed prevalence. Conversely, the average cost per cow, if the true prevalence was less than the presumed prevalence, was less than the cost based on a correctly presumed prevalence. For protocols 1 5, protocols 4 and 5 yielded the lowest average costs when presumed prevalences were lower or higher than true prevalences (Table ). The effect of differences between presumed and true prevalence was also examined considering the variation around the average costs, as illustrated by the 95% prediction intervals in Table 3. For example, for a herd tested using protocol 4 with a presumed prevalence of 1.0%, the range of possible costs, according to the 95% prediction interval, was from $1.7 to $3.68 if the presumed prevalence was correct (true prevalence 1.0%). However, if presumed prevalence was 1.0% and true prevalence of the herd was.0% or 3.0%, the cost was as high as $5.4 or $6.9, respectively (Table 3). The second situation examined involved no presumption of herd prevalence, and fixed pool size was used for all herds. For a population of herds tested using protocol 4, where herd prevalences were distributed assuming a beta distribution, as previously described (1% mode and 99% certainty that prevalence is 3%), the fixed pool size that yielded the lowest average cost per cow was 0 and * 5, with average cost per cow of $3.0 and 95% prediction limit of $1.36 $5.36. The fixed pool size that yielded the lowest upper prediction limit however was 1 and * 4, with average cost per cow of $3.8 and 95% prediction Table 3. Effect of differences between presumed and true prevalence of BVDV-infected cattle on cost per cow* using protocol 4. Presumed prevalence (%), * True prevalence (%) , 6 $1.7 $.69 $3.58 $4.40 $5.0 $5.78 ($0.90, $.66) ($1.56, $3.90) ($.3, $4.9) ($3.00, $5.9) ($3.68, $6.80) ($4.1, $7.34) , 5 $1.84 $.64 $3.38 $4.11 $4.8 $5.46 ($1.18, $.6) ($1.7, $3.68) ($.34, $4.54) ($.88, $5.4) ($3.5, $6.0) ($4.04, $6.9) , 4 $.33 $.97 $3.58 $4.19 $4.73 $5.5 ($1.8, $.94) ($.4, $3.78) ($.7, $4.56) ($3.0, $5.30) ($3.6, $5.9) ($4.10, $6.40) * Values are mean cost per cow (95% prediction interval). is first stage pool size, and * is second stage pool size.

7 Pooled testing to diagnose BVDV-PI 01 limits of $1.96 $5.18. Use of a fixed pool size was associated with less general uncertainty about the ranges of possible costs, as indicated by the generally lower upper prediction limits as compared with the upper prediction limits associated with an incorrectly presumed prevalence (Table 3). Discussion The protocols for pooled-sample testing presented here show how pooling strategies, using a sensitive diagnostic test such as PCR/probe, could offer a competitive and cost-effective diagnostic alternative for identification of BVDV-infected cattle. A pooling approach is expected to identify viremic animals at costs that are liely to be lower than those incurred by testing individual animals. As prevalence increases beyond 3%, however, the competitive benefit of pooledsample testing would be expected to diminish. Using protocol 4, which generally yielded the lowest costs, the average cost would increase substantially with increased prevalence ($5.5 for a true prevalence of 3% to $8.40 for a true prevalence of 6%), which would mae the cost of pooled-testing comparable to that of alternative assays, with anticipated cost per sample possibly as low as $8.00. Although prevalences above 3% do not seem liely when testing an entire herd for BVDV-PI, the higher costs of pooled testing for higher prevalences indicate that pooling from high-ris animal groups or use of pooling for routine diagnosis of clinical samples would not be expected to be cost effective because of the high probability of infection (prevalence) for these type of samples. Comparison of the cost per cow for protocols 1 5 using the least-cost pool size for a given true prevalence showed that the protocol that included repooled and split positive pools (protocol 5) yielded the lowest average cost per cow for prevalences between 0.5% and.0%, whereas repooling with no split (protocol 4) yielded the lowest average cost per cow for prevalences of.5% and 3%. The differences between the least average costs per cow for the protocols, however, were small. For a 1.0% prevalence, the least average cost per cow for protocol 4 ($.61) was only $0.08 more than that from protocol 5 ($.53). Protocol 4 may be preferred, therefore, even for prevalences.5% because protocol 4 would involve less laboratory handling of blood samples and would be expected to produce final results in a shorter time period that would protocol 5. Once a protocol is chosen, nowledge of the most probable herd prevalence of infection is required to tae full advantage of the pooled testing method and to obtain the lowest possible cost. If the presumed prevalence is higher (lower) than the true prevalence, the respective average costs anticipated as if the presumed prevalence were true would be lower (higher) than the actual costs associated with the true prevalence. As the difference between presumed and true prevalence increases, the difference between the anticipated average cost for the presumed prevalence and the actual average cost increases. Although use of a presumed prevalence that differs from the true prevalence would not tae full advantage of the lower cost of pooled testing, the average costs per cow incurred could still be lower than costs for individual testing. For example, in the extreme case examined here, if the presumed prevalence was 0.5% and the true prevalence was 3%, the average cost per cow using protocol 4 would be $5.78 (Table 3), which may still be lower than individual animal testing with other diagnostic assays. Factors to consider in establishing an appropriate diagnostic laboratory fee for pooled-sample testing include the degree of certainty about prevalence and the margin of error between the fee charged and the actual cost that could be observed. The difficulty in determining a standard fee when testing is performed using a presumption of the prevalence is the potential for an incorrectly presumed prevalence and random variation in cost from herd to herd. One option for determining a fee that considers these variations could be to use the highest probable cost. Using protocol 4, such a fee would be $7.34, which corresponds to the upper 95% prediction limit of the cost for a presumed prevalence of 0.5% and a true prevalence of 3.0% (Table 3) and would exceed laboratory costs most of the time. Another option would be to use a standard fee that would cover the costs for testing using a fixed pool size, regardless of prevalence. Testing all herds using protocol 4 with fixed pool sizes of 1 and * 4 and assuming the distribution described would yield a distribution of costs with a mean of $3.8 and lower and upper limits of $1.96 and $5.18. A fee of $3.8 would exceed the actual laboratory costs half of the time but would be lower the rest of the time, as opposed to a fee of $5.18, for example, which would exceed the actual observed costs 97.5% of the time. Advantages of this option would be the simplicity inherent in using the same pool size for all testing (as opposed to changing pool size for each herd situation) and the reduced uncertainty in the range of possible costs. Under field conditions, the cost per cow would differ from the estimates obtained here if infected animals were not randomly allocated to pools, as was assumed. Lac of random allocation might occur if infected animals are tested in some order based on a factor or attribute that is associated with infection, resulting in a subsequent clustering of positive samples in a few pools. For example, if for some reason heifers tended

8 0 Muñoz-Zanzi et al. to have a higher prevalence than cows and blood samples were collected and tested using groups of heifers and of cows, estimated costs per animal and 95% prediction intervals would no longer be valid because positive pools from the heifers would have more positive samples and positive pools from cows would have fewer positive samples than expected for a random allocation. Knowledge of differences in the prevalence of infection according to such attributes or covariates as age or previous exposure could be used to further refine methods proposed here and to improve the least-cost estimates. For example, samples of animals from each group having different presumed prevalences could be pooled according to the optimal pool size for their corresponding prevalences. Pooled testing of blood samples obtained at 1 point in time would identify viremic cattle, which liely represent persistent infection, but may include acute field infection or recent vaccination with modified live vaccine. To confirm BVDV-PI animals, as with other diagnostic assays for PI, a second positive sample taen 3 wees later would be necessary; such costs were not considered in the pooling costs reported here. Also, sensitivity and specificity of PCR will liely not be perfect, resulting in some probably low level of misclassification, either false-negative or false-positive results. In preliminary evaluation of the PCR used in this study, 35 animals identified as PI were tested by PCR and virus isolation. Thirty-four of the 35 were positive by both PCR and virus isolation, providing a PCR sensitivity of 100% if virus isolation is considered the gold standard. Samples provided from 1 cow maintained in a research herd b were negative by both PCR and virus isolation, providing a sensitivity of 97%, assuming the cow was PI and an intermittent shedder of virus. All individual samples positive by PCR were also detected using the pooling protocol described. Documentation of the sensitivity and specificity of PCR for detecting BVDV-PI based on a larger number of individual animals and sample pools is ongoing. In evaluating the ultimate cost effectiveness of pooling methodologies, the implication of imperfect sensitivity and specificity should be considered. The pooling methods described here for BVDV diagnosis have general and broad applications to veterinary diagnostics. Although new diagnostic technology such as PCR is nown for its extremely high detection limits, the cost has precluded routine use, especially for screening or surveillance. Use of these methods would permit large-scale use of the diagnostic power of the PCR, particularly under conditions of very low prevalence where cost of individual animal testing with conventional assays would be prohibitive. The use of pooling procedures has practical implications, not only to reduce laboratory and user costs but also to permit surveillance of populations for specific agents. Pooled-sample testing lends itself to screening and monitoring flocs or herds for low prevalence agents, as may be of interest in preharvest food safety programs, foreign animal disease surveillance, and herd or floc certification programs. Acnowledgements This wor was supported in part by funds provided by the US Department of Agriculture (Regional Research Project W-11 and Formula Funds), by a National Research Initiative Competitive Award ( ), by a bloc grant from the Graduate Group in Epidemiology, University of California, Davis, and by the American Association of University Women. 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